Lower Bound Analysis For Large Errors In Nonlinear State Estimation

This paper addresses the problem of estimating a state vector from a sequence of data generated by a nonlinear process. In particular, the effects of nonlinearity on performance bounds for large estimation errors are analyzed via the marginal density function. The use of local processing to produce a reduced data set, under conditions of asymptotic normality, provides a simple mechanism for formulating a likelihood function. Nonlinear estimation techniques are then applied to a reduced order system (reduced dimensionality), and an approximation of the marginal density is obtained with the corresponding error bounds. This method of hierarchical processing results in both computational efficiency and algorithm flexibility. As an illustrative example, simulated results are presented involving noisy and biased data. Deviations from the linear assumptions inherent in the use of the traditional Fisher information matrix (FIM) are explained.